10 papers
Transitivity and homogeneity of orthosets and the real Hilbert spaces
Thomas Vetterlein
An orthoset (also called an orthogonality space) is a set equipped with a symmetric and irreflexive binary relation , called the orthogonality relation. In quantum physi…
Linear orthogonality spaces as a new approach to quantum logic
Kadir Emir, David Kruml, Jan Paseka +1
The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as mi…
A geometric approach to Wigner-type theorems
Mark Pankov, Thomas Vetterlein
Let be a complex Hilbert space and let be the associated projective space (the set of rank-one projections). Suppose that . We prove the followin…
Categories of orthogonality spaces
Jan Paseka, Thomas Vetterlein
An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutu…
Gradual transitivity in orthogonality spaces of finite rank
Thomas Vetterlein
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an exam…
Reasoning with graded information: the case of diagnostic rating scales in healthcare
Thomas Vetterlein, Anna Zamansky
In medicine one frequently deals with vague information. As a tool for reasoning in this area, fuzzy logic suggests itself. In this paper we explore the applicability of the basic…